Departures from Gibrat's Law, Discontinuities and City Size Distributions

Abstract

Cities are complex, self-organising, evolving systems and the emergent patterns they manifest provide insight into the dynamic processes in urban systems. This article analyses city size distributions, by decade, from the south-eastern region of the US for the years 1860 -1990. It determines if the distributions are clustered into size classes and documents changes in the pattern of size classes over time. A statistical hypothesis test was also performed to detect dependence between city size and growth using discrete probability calculations under the assumption of Gibrat's law. The city size distributions for the south-eastern region of the US were discontinuous, with cities clustering into distinct size classes. The analysis also identified departures from Gibrat's law, indicating variable growth rates at different scales.

Panarchy: Discontinuities Reveal Similarities in the Dynamic System Structure of Ecological and Social Systems

“…Thus, if Gibrat's Law is not satisified, Zipf's Law cannot be satisfied. Garmestani et al (2007) found that growth rates differed by city size, in contrast to the distribution expected if Gibrat's Law held for this data set. On a regional level, the results indicated that city growth was not driven by small, random growth forces.…”

“…Rather, growth was correlated with size, with smaller cities exhibiting higher growth rates and larger cities exhibiting lower growth rates ). The results reported in Garmestani et al (2007) indicated that discrete size classes in city size distributions emerged as a result of size-dependent growth at the available scales of opportunity within urban systems.…”

“…Using Bessey's data, Garmestani et al (2007) performed a statistical hypothesis test upon Ecology and Society 14(1): 15 http://www.ecologyandsociety.org/vol14/iss1/art15/ rank-size city data from the southeastern region of the United States under the assumptions of Gibrat's Law (Gibrat 1957). Zipf's Law manifests when all central places in an urban hierarchy have sizeinvariant growth rates.…”

Power laws, discontinuities and regional city size distributions

“…This analysis builds upon Bessey, who identified departures from Zipf's Law for cities in the southeastern and southwestern regions of the U.S. Utilizing this same data, Garmestani et al (2007) found departures from Gibrat's law, in that city growth is correlated to size, with smaller cities exhibiting faster growth rates and larger cities exhibiting slower growth rates. In addition, Garmestani et al (2008) analyzed this data and found that cities in the southeastern U.S. self-organize into discrete size classes, much as they were found to do in the southwestern U.S. (Garmestani et al, 2005).…”

“…Sharma (2003) found that cities in India had periods of size-independent growth as well as periods of size-dependent growth. Garmestani et al (2007) found that regional city size distributions in the U.S. exhibited size-dependent growth rates. Utilizing time series data, they found that smaller cities grow faster than average, and larger cities grow slower than average.…”